Metalens-integrated optical engine

ABSTRACT

A metalens-integrated optical engine includes a plurality of light source modules, a collimating and deflecting module and a light-combining module. Each of the light source modules emits a light beam. The collimating and deflecting meta optical members is for collimating and deflecting the light beams such that the light beams are collimated and deflected and travel to a predetermined position. The light-combining module includes a light-combining meta optical array that is located at the predetermined position, that receives the light beams via the collimating and deflecting module, and that deflects the light beams, so as to combine the non-parallel light beams into a single light beam.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to Taiwanese Invention PatentApplication No. 110140442, filed on Oct. 29, 2021.

FIELD

The disclosure relates to an optical device, and more particularly to ametalens-integrated optical engine.

BACKGROUND

Referring to FIG. 1 , a conventional optical engine includes three lightsources 11 (e.g., red (R), green (G) and blue (B)), three collimatinglenses 12 each of which is located on the light path of a respective oneof the light sources 11, and three beam splitters 13 that respectivelycorrespond to the light paths of the light sources 11. In FIG. 1 , theleftmost beam splitter 13 reflects red light (or all lights), the middlesplitter 13 reflects green light and permits the red light to traveltherethrough, and the rightmost splitter 13 reflects blue light andpermits the red light and the green light to travel therethrough. Assuch, the red light, the green light and the blue light are combined toform white light.

However, the sizes of the abovementioned collimating lenses 12 and beamsplitters 13 are relatively large. In order to reduce the size of theconventional optical engine, the distances among the light sources 11and the sizes of the optical components should be reduced. Themanufacturing precision of relatively small collimating lenses isdifficult to maintain. Higher precision of positioning among relativelysmall optical components during assembly of the optical components isrequired to be higher. Thus, with current technical limitations, thesize of the conventional optical engine is very difficult to reduce.However, smaller optical engines are in heavy demanded due to the growthof applications including augmented reality (AR), virtual reality (VR)and micro projection.

SUMMARY

Therefore, an object of the disclosure is to provide ametalens-integrated optical engine that can alleviate at least one ofthe drawbacks of the prior art

According to an aspect of the disclosure, the metalens-integratedoptical engine includes a plurality of light source modules, acollimating and deflecting module and a light-combining module. Each ofthe light source modules emits a light beam with particular wavelength.The collimating and deflecting module includes a plurality ofcollimating and deflecting meta optical members each of which is locatedon the path of the light beam emitted by a respective one of the lightsource modules. The collimating and deflecting meta optical members isfor collimating and deflecting the light beams emitted by the lightsource modules such that the light beams emitted by the light sourcemodules are collimated and deflected and travel to a predeterminedposition. The light-combining module includes a light-combining metaoptical member that is located at one side of the collimating anddeflecting module opposite to the light source modules. Thelight-combining meta optical member includes a light-combining metaoptical array that is located at the predetermined position, thatreceives the light beams collimated and deflected via the collimatingand deflecting module, and that deflects the light beams based onwavelengths and angles of incidence, so as to combine the non-parallellight beams into a single light beam.

According to another aspect of the disclosure, the metalens-integratedoptical engine includes a plurality of light source modules, acollimating and deflecting module, a shaping module and alight-combining module. Each of the light source modules emits a lightbeam with particular wavelength. The collimating and deflecting moduleincludes a plurality of collimating and deflecting meta optical memberseach of which is located on the path of the light beam emitted by arespective one of the light source modules. The collimating anddeflecting meta optical members is for collimating and deflecting thelight beams emitted by the light source modules such that the lightbeams emitted by the light source modules are collimated and deflectedand travel to a predetermined position. Each of the collimating anddeflecting meta optical members includes a substrate that has a surfaceextending along an X-axis and a Y-axis, and a collimating and deflectingmeta optical array that is disposed on the surface, that permitsincidence of the light beams emitted by the respective one of the lightsource modules, and that includes a plurality of nanostructures arrangedin an array. Each of the nanostructures extends along a Z-axis that isperpendicular to the surface. The nanostructures of the collimating anddeflecting meta optical array of n-th collimating and deflecting metaoptical member satisfy a phase shift formula relative to a center of anoptical axis:

${\Delta{\varphi_{nC}\left( {x_{n},y_{n}} \right)}} = {{{- \frac{2\pi}{\lambda_{n}}}\left( {\sqrt{x_{n}^{2} + f_{xcn}^{2}} - f_{xcn} + \sqrt{y_{n}^{2} + f_{ycn}^{2}} - f_{ycn} - {\left( {{x_{n}\cos\theta_{n}} + {y_{n}\sin\theta_{n}}} \right)\sin\gamma_{n}}} \right)} - {\Delta{\Phi_{nC}\left( {x_{n},y_{n}} \right)}{wherein}}}$${{\Delta{\Phi_{nC}\left( {x_{n},y_{n}} \right)}} = {\frac{2\pi}{\lambda_{n}}{\sum_{i = 0}^{\infty}{\sum_{j = 0}^{\infty}{a_{nij}x_{n}^{2i}y_{n}^{2j}}}}}},$

and 2i+2j≥4. n denotes all positive integers no greater than N, and N isthe number of the collimating and deflecting meta optical members,Δϕ_(nC)(x_(n), y_(n)) denotes the phase shift of n-th light beamrelative to the center of an optical axis of the collimating anddeflecting meta optical array of n-th collimating and deflecting metaoptical member generated by the collimating and deflecting meta opticalarray of n-th collimating and deflecting meta optical member. An originof the coordinate system is defined to be the center of the optical axisof the collimating and deflecting meta optical array of n-th collimatingand deflecting meta optical member. Δϕ_(nC)(0,0)=0. (x_(n), y_(n))denotes the position of each of the nanostructures of the collimatingand deflecting meta optical array of n-th collimating and deflectingmeta optical member in the coordinate system. λ_(n) is the wavelength ofn-th light beam. f_(xcn) is the focal length of the collimating anddeflecting meta optical array along the X-axis. f_(ycn) is the focallength of the collimating and deflecting meta optical array along theY-axis. θ_(n) is the angle formed between the X-axis and the imaginglight beam of n-th light beam. γ_(n) is the angle formed between theZ-axis and the imaging light beam of n-th light beam.ΔΦ_(nC)(x_(n),y_(n)) is high-order term, and is for compensating thephase shift of high-order optical aberration. α_(nij) are predeterminedcoefficients. The shaping module includes a plurality of shaping metaoptical arrays. Each of the shaping meta optical arrays is disposed on adisposing surface of a respective one of the collimating and deflectingmeta optical members for shaping the light beams emitted by therespective one of the light source modules. The light-combining modulereceives the light beams collimated and deflected via the collimatingand deflecting module, and combines the non-parallel light beams into asingle light beam.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages of the disclosure will become apparent inthe following detailed description of the embodiments with reference tothe accompanying drawings, of which:

FIG. 1 is a schematic view illustrating a conventional optical engine;

FIG. 2 is a schematic view illustrating an embodiment of themetalens-integrated optical engine according to the disclosure;

FIG. 3 is a schematic view illustrating light beams travelling in theembodiment;

FIG. 4 is another schematic view illustrating the light beams travellingin the embodiment;

FIG. 5 is a schematic view illustrating a shaping module shaping thelight beams;

FIG. 6 is a schematic view illustrating the shaping module and acollimating and deflecting module;

FIGS. 7 to 9 are fragmentary perspective views illustrating the shapingmodule, wherein FIGS. 8 and 9 are enlarged views of regions A and B ofFIG. 7 ;

FIGS. 10 to 12 are fragmentary perspective views illustrating theshaping module of another example, wherein FIGS. 11 and 12 are enlargedviews of regions C and D of FIG. 10 ;

FIG. 13 is a top view illustrating the embodiment used in a projector;and

FIG. 14 is a perspective view illustrating the embodiment used in theprojector.

DETAILED DESCRIPTION

Before the disclosure is described in greater detail, it should be notedthat where considered appropriate, reference numerals or terminalportions of reference numerals have been repeated among the figures toindicate corresponding or analogous elements, which may optionally havesimilar characteristics.

Referring to FIG. 2 , an embodiment of the metalens-integrated opticalengine according to the disclosure includes a plurality of light sourcemodules 2, a collimating and deflecting module 3 and a light-combiningmodule 4. In some embodiments, the metalens-integrated optical enginemay further include a shaping module 5. The metalens-integrated opticalengine may include the shaping module 5 for shaping light beams whenbeing used in augmented reality (AR) and virtual reality (VR)applications, however, when the metalens-integrated optical engine isused in micro projection, the shaping module 5 may be omitted.

Each of the light source modules 2 emits a light beam with particularwavelength(s). There are three light source modules 2 in thisembodiment. The light source modules 2 emit red light, green light andblue light, respectively. The number of the light source modules 2 andthe wavelength(s) of the lights emitted by the light source modules 2may vary according to practical requirements, and may not be limited bythese embodiments. In one embodiment, the light source module 2 may beconfigured as a laser light source, which has high frequency modulationand narrowband characteristics.

Referring to FIGS. 2 and 3 , the collimating and deflecting module 3includes a plurality of collimating and deflecting meta optical members31 each of which is located on the path of the light beam emitted by arespective one of the light source modules 2. The collimating anddeflecting meta optical members 31 are for collimating and deflectingthe light beams emitted by the light source modules 2 such that thelight beams emitted by the light source modules 2 are collimated anddeflected, and travel to a predetermined position on the light-combiningmodule 4.

Each of the collimating and deflecting meta optical members 31 includesa substrate 311 and a collimating and deflecting meta optical array (notshown).

The substrate 311 of each of the collimating and deflecting meta opticalmembers 31 has a surface 312 that extends along an X-axis (see X₁ to X₃in FIG. 3 ) and a Y-axis (see Y₁ to Y₃ in FIG. 3 ).

The collimating and deflecting meta optical array of each of thecollimating and deflecting meta optical members 31 is disposed on thesurface 312 of the collimating and deflecting meta optical member 31,permits incidence of the light beams emitted by the respective one ofthe light source modules 2, and includes a plurality of nanostructures(not shown) that are arranged in an array. Each of the nanostructuresextends along a Z-axis (see Z₁ to Z₃ in FIG. 3 ) that is perpendicularto the surface 312.

The nanostructures of the collimating and deflecting meta optical arrayof n-th collimating and deflecting meta optical member 31 satisfy thephase shift formula relative to a center of an optical axis:

$\begin{matrix}{{{{\Delta{\varphi_{nC}\left( {x_{n},y_{n}} \right)}} = {{{- \frac{2\pi}{\lambda_{n}}}\left( {\sqrt{x_{n}^{2} + y_{n}^{2} + f_{n}^{2}} - f_{n} - {\left( {{x_{n}\cos\theta_{n}} + {y_{n}\sin\theta_{n}}} \right)\sin\gamma_{n}}} \right)} - {\Delta{\Phi_{nC}\left( {x_{n},y_{n}} \right)}}}};{Wherein}},} & \left( {{Formula}1} \right)\end{matrix}$${{\Delta{\Phi_{nC}\left( {x_{n},y_{n}} \right)}} = {\frac{2\pi}{\lambda_{n}}{\sum_{i = 0}^{\infty}{\sum_{j = 0}^{\infty}{a_{nij}x_{n}^{2i}y_{n}^{2j}}}}}},{{{{and}2i} + {2j}} \geq 4.}$

i=0,1,2, . . . , j=0,1,2, . . . , 2i+2j denotes order, and the condition2i+2j≥4 is to compensate the phase shift of the 4th order or higher.

Wherein, n denotes all positive integers no greater than N, and N is thenumber of the collimating and deflecting meta optical members 31.Δϕ_(nC)(x_(n),y_(n)) denotes the phase shift of n-th light beam (i.e.,the light beam emitted by n-th light source module 2) relative to thecenter of the optical axis of the collimating and deflecting metaoptical array of n-th collimating and deflecting meta optical member 31generated by the collimating and deflecting meta optical array of n-thcollimating and deflecting meta optical member 31. The origin (0, 0) ofthe coordinate system is defined to be the center of the optical axis ofthe collimating and deflecting meta optical array of n-th collimatingand deflecting meta optical member 31. Δϕ_(nC)(0,0)=0. (x_(n),y_(n))denotes the position of each of the nanostructures of the collimatingand deflecting meta optical array of n-th collimating and deflectingmeta optical member 31 in the coordinate system. λ_(n) is the wavelengthof n-th light beam. f_(n) is the focal length of n-th light beam. θ_(n)is the angle formed between the X-axis and the imaging light beam ofn-th light beam. y_(n) is the angle formed between the Z-axis and theimaging light beam of n-th light beam. ΔΦ_(nC)(x_(n),y_(n)) ishigh-order term, and is specifically for compensating the phase shift of4th order or higher order optical aberration in this embodiment. α_(nij)are predetermined coefficients (i.e., coefficients of polynomial).

The first half portion of Formula 1

${- \frac{2\pi}{\lambda_{n}}}\left( {\sqrt{x_{n}^{2} + y_{n}^{2} + f_{n}^{2}} - f_{n} - {\left( {{x_{n}\cos\theta_{n}} + {y_{n}\sin\theta_{n}}} \right)\sin\gamma_{n}}} \right)$

depicts an ideal state of an optical system in which no opticalaberration exists. However, a general optical system contains high-orderoptical aberration. When an optical system demands higher resolution,ΔΦ_(nC)(x_(n),y_(n)) serves to compensate the phase shift of thehigh-order optical aberration.

When an optical system contains 4th order and/or higher order opticalaberration that needs to be compensated, the coefficients of polynomialα_(nij) can be found by conventional automatic optimization methods, soas to obtain the value of ΔΦ_(nC)(x_(n),y_(n)). When the 4th orderand/or higher order optical aberration of an optical system need not becompensated, the coefficients of polynomial α_(nij) are zero, and thevalue of ΔΦ_(nC)(x_(n),y_(n)) is zero.

For example, if a parallel glass plate with a thickness of t has arefractive index of n_(λ) _(n) , and a light beam has an image distanceof l after travelling through the glass plate, the glass plate wouldgenerate the 4th order term (α_(n20)x⁴, α_(n11)x²y², α_(n02)y⁴) opticalaberration. When the optical aberration is generated in an opticalsystem with n=1, the coefficients can be derived by analysis:

$\begin{matrix}{a_{120} = {a_{102} = {{\frac{1}{2}a_{111}} = {- \frac{\left( {n_{\lambda n}^{2} - 1} \right)t}{8n_{\lambda_{n}}^{3}l^{4}}}}}} & \left( {{Formula}2} \right)\end{matrix}$

If other high-order optical aberration is to be compensated, acorresponding phase shift ΔΦ_(nC)(x_(n),y_(n)) can be obtained by theformula to compensate for the optical aberration. When the high-orderoptical aberration need not be compensated, the coefficients ofpolynomial α_(nij) are zero.

The setup of the nanostructures of the collimating and deflecting metaoptical arrays of the collimating and deflecting meta optical members 31can be referred to in Taiwanese Invention Patent Application No.110126860.

It should be noted that, when the metalens-integrated optical engineincludes the shaping module 5, the formula of the phase shift should bemodified, and would be described in the following paragraphs.

Referring to FIGS. 2 and 4 , the light-combining module 4 is located atone side of the collimating and deflecting module 3 opposite to thelight source modules 2, receives the light beams collimated anddeflected via the collimating and deflecting module 3, and deflects thelight beams, so as to combine the light beams into a single light beam.The light-combining module 4 may be implemented by conventional opticalcomponents (e.g., dichroic filter(s) or prism(s)). In this embodiment,the light-combining module 4 is implemented by meta opticalcomponent(s).

The light-combining module 4 includes a light-combining meta opticalmember 40 that is located at one side of the collimating and deflectingmodule 3 opposite to the light source modules 2. The light-combiningmeta optical member 40 includes a substrate 41 and a light-combiningmeta optical array (not shown). The light-combining meta optical arrayis located at the predetermined position on the light-combining module4, receives the light beams collimated and deflected via the collimatingand deflecting module 3, and deflects the light beams based onwavelengths and angles of incidence, so as to combine the non-parallellight beams into a single light beam.

The substrate 41 has a surface 411 that extends along an X-axis and aY-axis.

The light-combining meta optical array is disposed on the surface 411,permits incidence of the light beams collimated and deflected via thecollimating and deflecting module 3, and includes a plurality ofnanostructures (not shown) that are arranged in an array. Each of thenanostructures extends along a Z-axis that is perpendicular to thesurface 411.

The nanostructures of the light-combining meta optical array of thelight-combining meta optical member 40 satisfy the phase shift formularelative to a center of an optical axis:

$\begin{matrix}{{\Delta{\varphi_{nL}\left( {x,y} \right)}} = {\frac{2\pi}{\lambda_{n}}\left( {{x\cos\theta_{n}} + {y\sin\theta_{n}}} \right)\sin\gamma_{n}}} & \left( {{Formula}3} \right)\end{matrix}$

Wherein, n denotes all positive integers no greater than N, and N is thenumber of the collimating and deflecting meta optical members 31.Δϕ_(nL)(x,y) denotes the phase shift of n-th light beam (labelled by L₁,L₂ and L₃ in FIG. 4 ) relative to the center of the optical axis of thelight-combining meta optical array generated by the light-combining metaoptical array. The origin (0, 0) of the coordinate system is defined tobe the center of the optical axis of the light-combining meta opticalarray. Δϕ_(nL)(0,0)=0. (x,y) denotes the position of each of thenanostructures of light-combining meta optical array in the coordinatesystem. λ_(n) is the wavelength of n-th light beam. θ_(n) is the angleformed between the X-axis and the incident light beam of n-th lightbeam. γ_(n) is the angle formed between the Z-axis and the incidentlight beam of n-th light beam.

The setup of the nanostructures of the light-combining meta opticalarrays of the light-combining module 4 can be referred to in TaiwaneseInvention Patent Application No. 110126861.

Referring to FIGS. 2 and 5 to 9 , the shaping module 5 is for shapingthe light beams. With particular reference to FIG. 5 , the shapingmodule 5 shapes a light beam such that the light beam has an ellipticcross-section at an incident surface and has a circular cross-section atan exit surface. The adjustment to the shape of the cross-section of thelight beam may depend on practical requirements, and is not limited tosuch.

The shaping module 5 includes a plurality of shaping meta optical arrays51. Each of the shaping meta optical arrays 51 is disposed on adisposing surface of a respective one of the collimating and deflectingmeta optical members 31, permits incidence of the light beam emitted bythe respective one of the light source modules 2, and includes aplurality of nanostructures 511 that are arranged in an array. Each ofthe shaping meta optical arrays 51 has a coordinate system that has anX-axis, a Y-axis and a Z-axis, and the disposing surface of therespective one of the collimating and deflecting meta optical members 31extends along the X-axis and the Y-axis. Each of the nanostructures 511extends along a Z-axis that is perpendicular to the disposing surface.

The nanostructures 511 of n-th shaping meta optical array 51 satisfy thephase shift formula relative to a center of an optical axis:

$\begin{matrix}{{{\Delta\varphi}_{nS}\left( {x_{n},y_{n}} \right)} = {\frac{2\pi}{\lambda_{n}}\left( {\sqrt{x_{n}^{2} + f_{xn}^{2}} - f_{xn} + \sqrt{y_{n}^{2} + f_{yn}^{2}} - f_{yn}} \right)}} & \left( {{Formula}4} \right)\end{matrix}$ −ΔΦ_(nS)(x_(n), y_(n));${Wherein},{{{\Delta\Phi}_{nS}\left( {x_{n},y_{n}} \right)} = {\frac{2\pi}{\lambda_{n}}{\sum_{i = 0}^{\infty}{\sum_{j = 0}^{\infty}{b_{nij}x_{n}^{2i}y_{n}^{2j}}}}}},{and}$2i + 2j ≥ 4.

i=0, 1, 2, . . . , j=0, 1, 2, . . . , 2i+2j denotes order, and thecondition 2i+2j≥4 is to compensate the phase shift of the 4th order orhigher.

Wherein, n denotes all positive integers no greater than N, and N is thenumber of the collimating and deflecting meta optical members 31.Δϕ_(nS)(x_(n),y_(n)) denotes the phase shift of n-th light beam (i.e.,the light beam emitted by n-th light source module 2) relative to thecenter of optical axis of n-th shaping meta optical array 51 generatedby n-th shaping meta optical array 51. The origin (0, 0) of thecoordinate system is defined to be the center of optical axis of n-thshaping meta optical array 51. Δϕ_(nS)(0,0)=0. (x_(n),y_(n)) denotes theposition of each of the nanostructures of n-th shaping meta opticalarray 51 in the coordinate system. λ_(n) is the wavelength of n-th lightbeam. f_(xn) is the focal length of n-th light beam along the X-axis.f_(yn) is the focal length of n-th light beam along the Y-axis.ΔΦ_(nS)(x_(n),y_(n)) is a high-order term, and is for compensating thephase shift of high-order optical aberration. b_(nij) are predeterminedcoefficients (i.e., coefficients of polynomial).

When an optical system contains 4th order and/or higher order (2i+2j≥4)optical aberration to be compensated, the coefficients of polynomialb_(nij) can be found by conventional automatic optimization methods, soas to obtain the value of ΔΦ_(nS)(x_(n),y_(n)). When the high-orderoptical aberration of an optical system need not be compensated, thecoefficients of polynomial b_(nij) are zero, and the value ofΔΦ_(nS)(x_(n),y_(n)) is zero.

In this embodiment, the number of the light source modules 2 is threeand the number of the collimating and deflecting meta optical members 31is three, so N=3, and n=1,2,3. The shaping meta optical arrays 51respectively satisfy three phase shift formulas (i.e., n=1,2,3). n maybe positive integers no greater than another integer. For example, inone embodiment, the number of the light source modules 2 is two and thenumber of the collimating and deflecting meta optical members 31 is two,so N=2, n=1,2, and the shaping meta optical arrays 51 respectivelysatisfy two phase shift formulas.

The phase shift formula of each of the shaping meta optical arrays 51relative to the center of the optical axis is described in the followingparagraphs.

For convenience, the three shaping meta optical arrays 51 arerespectively named first shaping meta optical array 51, second shapingmeta optical array 51 and third shaping meta optical array 51.

The nanostructures 511 of the first shaping meta optical array 51satisfy the phase shift formula as follows:

$\begin{matrix}{{{\Delta\varphi}_{1S}\left( {x_{1},y_{1}} \right)} = {\frac{2\pi}{\lambda_{1}}\left( {\sqrt{x_{1}^{2} + f_{x1}^{2}} - f_{x1} + \sqrt{y_{1}^{2} + f_{y1}^{2}} - f_{y1}} \right)}} & \left( {{Formula}5} \right)\end{matrix}$ −ΔΦ_(1S)(x₁, y₁);

Wherein, Δϕ_(1S)(x₁,y₁) denotes the phase shift of the first light beam(i.e., red light (R), wavelength=640 nm) relative to the center of theoptical axis of the first shaping meta optical array 51 generated by thefirst shaping meta optical array 51. The origin (0, 0) of the coordinatesystem is defined to be the center of the optical axis of the firstshaping meta optical array 51. Δϕ_(1S)(0,0)=0. (x₁,y₁) denotes theposition of each of the nanostructures 511 of the first shaping metaoptical array 51 in the coordinate system. λ₁ is the wavelength of thefirst light beam. f_(x1) is the focal length of the first light beamalong the X-axis. f_(y1) is the focal length of the first light beamalong the Y-axis.

The nanostructures 511 of the second shaping meta optical array 51satisfy the phase shift formula as follows:

$\begin{matrix}{{{\Delta\varphi}_{2S}\left( {x_{2},y_{2}} \right)} = {\frac{2\pi}{\lambda_{2}}\left( {\sqrt{x_{2}^{2} + f_{x2}^{2}} - f_{x2} + \sqrt{y_{2}^{2} + f_{y2}^{2}} - f_{y2}} \right)}} & \left( {{Formula}6} \right)\end{matrix}$ −ΔΦ_(2S)(x₂, y₂);

Wherein, Δϕ_(2S)(x₂,y₂) denotes the phase shift of the second light beam(i.e., green light (G), wavelength=520 nm) relative to the center of theoptical axis of the second shaping meta optical array 51 generated bythe second shaping meta optical array 51. The origin (0, 0) of thecoordinate system is defined to be the center of the optical axis of thesecond shaping meta optical array 51. Δϕ_(2S)(0,0)=0. (x₂,y₂) denotesthe position of each of the nanostructures 511 of the second shapingmeta optical array 51 in the coordinate system. λ₂ is the wavelength ofthe second light beam. f_(x2) is the focal length of the second lightbeam along the X-axis. f_(y2) is the focal length of the second lightbeam along the Y-axis.

The nanostructures 511 of the third shaping meta optical array 51satisfy the phase shift formula as follows:

$\begin{matrix}{{{\Delta\varphi}_{3S}\left( {x_{3},y_{3}} \right)} = {\frac{2\pi}{\lambda_{3}}\left( {\sqrt{x_{3}^{2} + f_{x3}^{2}} - f_{x3} + \sqrt{y_{3}^{2} + f_{y3}^{2}} - f_{y3}} \right)}} & \left( {{Formula}7} \right)\end{matrix}$ −ΔΦ_(3S)(x₃, y₃);

Wherein, Δϕ_(3S)(x₃,y₃) denotes the phase shift of the third light beam(i.e., blue light (B), wavelength=450nm) relative to the center of theoptical axis of the third shaping meta optical array 51 generated by thethird shaping meta optical array 51. The origin (0, 0) of the coordinatesystem is defined to be the center of the optical axis of the thirdshaping meta optical array 51. Δϕ_(3S)(0,0)=0. (x₃,y₃) denotes theposition of each of the nanostructures 511 of the third shaping metaoptical array 51 in the coordinate system. λ₃ is the wavelength of thethird light beam. f_(x3) is the focal length of the third light beamalong the X-axis. f_(y3) is the focal length of the third light beamalong the Y-axis.

When the metalens-integrated optical engine includes the shaping module5, the phase shift formula(s) (Formula 1) of the collimating anddeflecting meta optical arrays of the collimating and deflecting metaoptical members 31 need to be modified such that the X-axis and theY-axis simultaneously generate collimated light. The modified phaseshift formula is as follows:

$\begin{matrix}{{{\Delta\varphi}_{nC}\left( {x_{n},y_{n}} \right)} =} & \left( {{Formula}8} \right)\end{matrix}$$- \frac{2\pi}{\lambda_{n}}\left( {\sqrt{x_{n}^{2} + f_{xcn}^{2}} - f_{xcn} + \sqrt{y_{n}^{2} + f_{ycn}^{2}} - f_{ycn} -} \right.$(x_(n)cos θ_(n) + y_(n)sin θ_(n))sin γ_(n)) − ΔΦ_(nC)(x_(n), y_(n));${Wherein},{{{\Delta\Phi}_{nC}\left( {x_{n},y_{n}} \right)} = {\frac{2\pi}{\lambda_{n}}{\sum_{i = 0}^{\infty}{\sum_{j = 0}^{\infty}{a_{nij}x_{n}^{2i}y_{n}^{2j}}}}}},{and}$2i + 2j ≥ 4.

i=0,1,2 . . . , j=0,1,2, . . . , 2i+2j denotes order, and the condition2i+2j≥4 is to compensate the phase shift of the 4th order or higher.

f_(xcn) is the focal length of the collimating and deflecting metaoptical array along the X-axis. f_(ycn) is the focal length of thecollimating and deflecting meta optical array along the Y-axis. Whenhigh-order optical aberration of an optical system need not becompensated, the coefficients of polynomial α_(nij) are zero, and thevalue of ΔΦ_(nC)(x_(n),y_(n)) is zero.

The focal lengths f_(xn), f_(yn) of each of the shaping meta opticalarrays 51 must cooperate with the focal lengths f_(xcn), f_(ycn) of thecollimating and deflecting meta optical array of the respective one ofthe collimating and deflecting meta optical members 31 to preventastigmatic aberration. Therefore, the focal length f_(n) in Formula 1should be fractioned into f_(xcn) and f_(ycn) with respect to X-axis andY-axis, respectively, so that the shaping meta optical arrays 51 and thecollimating and deflecting meta optical members 31 cooperatively shapeand collimate the light beams, and generate collimated light beam atX-axis and Y-axis, simultaneously.

For the collimating and deflecting meta optical array of each of thecollimating and deflecting meta optical members 31 and the respectiveone of the shaping meta optical arrays 51, the relationship among thefocal lengths f_(xcn), f_(ycn) of the collimating and deflecting metaoptical array and the focal lengths f_(xn), f_(yn) of the shaping metaoptical array 51 are as follows:

$\begin{matrix}{{f_{ycn} = \frac{d \cdot {f_{ytn}\left( {d - f_{xn}} \right)}}{{f_{ytn}\left( {d - f_{xn}} \right)} - {f_{xn}\left( {d - f_{xtn}} \right)}}};} & \left( {{Formula}9} \right)\end{matrix}$ $\begin{matrix}{{f_{xn} = \frac{f_{xcn} - d}{\frac{f_{xcn}}{f_{xtn}} - 1}};} & \left( {{Formula}10} \right)\end{matrix}$ $\begin{matrix}{{f_{yn} = \frac{d \cdot {f_{xn}\left( {d - f_{xtn}} \right)}}{{d\left( {d - f_{ytn}} \right)} - {f_{xn}\left( {f_{xtn} - f_{ytn}} \right)}}};} & \left( {{Formula}11} \right)\end{matrix}$ $\begin{matrix}{{d = \frac{d_{\mathcal{g}}}{n_{\mathcal{g}}}};} & \left( {{Formula}12} \right)\end{matrix}$

Wherein: f_(xtn), f_(ytn) are synthesized focal lengths respectivelyalong X-axis and Y-axis synthesized by the collimating and deflectingmeta optical array and the shaping meta optical array 51; d isequivalent to air thickness between the collimating and deflecting metaoptical array and the shaping meta optical array 51; d_(g) is thedistance between the collimating and deflecting meta optical array andthe shaping meta optical array 51; and n_(g) is the refractive index ofthe medium between the collimating and deflecting meta optical array andthe shaping meta optical array 51.

Since the collimating and deflecting meta optical array of each of thecollimating and deflecting meta optical members 31 and the respectiveone of the shaping meta optical arrays 51 cooperatively shape andcollimate light beam(s) simultaneously with respect to the X-axis andthe Y-axis, after the synthesized focal lengths f_(xtn), f_(ytn) areset, once one of the focal lengths f_(xcn), f_(ycn) of the collimatingand deflecting meta optical array and the focal lengths f_(xn), f_(yn)of the shaping meta optical array 51 is determined, the other three ofthe focal lengths f_(xcn), f_(ycn) of the collimating and deflectingmeta optical array and the focal lengths f_(xn), f_(yn) of the shapingmeta optical array 51 can be determined by formulas 9 to 11, so as tosimultaneously accomplish collimation and shaping with respect to theX-axis and the Y-axis.

The functions, characteristics and method for preparing themetalens-integrated optical engine according to the disclosure aredescribed as follows:

-   -   I. Nanostructure.

In this embodiment, the substrates are made of SiO₂. The nanostructuresof each of the meta optical arrays are made of TiO₂, and are eachconfigured as a pillar that has a rectangular cross-section taken alongX-Y plane. The dimensions of each of the nanostructures correspond tothe wavelength of n-th light beam. Specifically, for each of thenanostructures, the length is

${\left. \frac{\lambda_{n}}{30} \right.\sim\lambda_{n}},$

the width is

${\left. \frac{\lambda_{n}}{30} \right.\sim\lambda_{n}},$

and the height is

${\left. \frac{\lambda_{n}}{100} \right.\sim 2}{\lambda_{n}.}$

It should be noted that, in another example, the cross-section of eachof the nanostructures taken along X-Y plane may be square, circular orpolygonal (triangular, pentagonal, hexagonal, etc.), and each of thenanostructures taken along X-Y plane may be hollow or solid, as long asthe nanostructures satisfy the phase shift formulas mentioned above.

-   -   II. The relationship between the phase and the nanostructures        (the material of the substrates is SiO₂; the material of the        nanostructures is TiO₂; the height along the Z-axis of each of        the nanostructures is 750 nm; the period of the optical arrays        on X-Y plane (i.e., the distance between centers of two adjacent        nanostructures) is 210 nm).

TABLE 1 relationship between the phase and the nanostructures LengthLength along along phase of phase of X- Y- X- Y- axis axis polarizationpolarization nanostructure (nm) (nm) (°) (°) nanostructure 50 50 17.717.7 (with respect 50 100 34.1 51.5 to the first 50 150 45.5 106.3 lightbeam 100 50 51.5 34.1 having 100 100 9.1 97.1 wavelength 100 150 129.6194.2 of 640 nm) nanostructure 50 50 24.9 24.9 (with respect 50 100 46.874.3 to the second 50 150 61.9 159.6 light beam 100 50 74.3 46.8 having100 100 146.5 146.5 wavelength 100 150 199.5 301.3 of 520 nm)nanostructure 50 50 33.6 33.6 (with respect 50 100 62.9 108.3 to thethird 50 150 82.9 242.0 light beam 100 50 108.3 62.9 having 100 100226.2 226.2 wavelength 100 150 315.2 107.9 of 450 nm)

It should be noted that the table above is exemplary only. One skilledin the art could make nanostructures of other sizes according to thecontent of the table.

Referring to FIGS. 7 to 9 , the relationship between the phase and thenanostructures above are presented by the polarization characteristicswith respect to X-axis and Y-axis, and is defined by the lengths alongX-axis and Y-axis. The phase shift is determined with respect toX-polarization and Y-polarization. Referring to FIGS. 10 to 12 , phaseof left-handed circularly polarized light and right-handed circularlypolarized light can be defined by Pancharatnam-Berry phase, in which thephase is defined by the geometric sizes of the pillars and the rotatedangles of the pillars, so as to obtain the phase shift of left-handedcircularly polarized light and right-handed circularly polarized light.However, each of the X-polarization, Y-polarization, the left-handedcircularly polarized light and the right-handed circularly polarizedlight is suitable for the abovementioned phase shift formulas ofΔϕ_(nC)(x_(n),y_(n)), Δϕ_(nL)(x_(n),y_(n)), Δϕ_(nS)(x_(n), y_(n)). (Inthe following paragraphs, Δϕ_(n)(x_(n),y_(n)) is used to refer to thesephase shifts)

-   -   III. Method for preparing the metalens-integrated optical engine        according to the disclosure.

Step 1):

Referring to FIG. 2 , calculate the phase shift Δϕ_(n)(x_(n),y_(n)) ateach position of each meta optical array by virtue of the phase shiftformulas respectively corresponding to the collimating and deflectingmodule 3, the light-combining module 4 and the shaping module 5, anddetermine the phase (ϕ_(n)(0,0)) at the origin of each meta opticalarray, so as to obtain the phase ϕ_(n)(x_(n),y_(n)) at each position,and fabricate the nanostructure corresponding to the phaseϕ_(n)(x_(n),y_(n)) according to Table 1.

For example, a nanostructure with the phase of a center of an opticalaxis thereof ϕ_(n)(0,0)=α is fabricated according to Table 1, and thephase shift Δϕ_(n)(x_(n),y_(n)) is b after calculation via the formulas.Then, ϕ_(n)(x_(n),y_(n))=a+b.

Step 2):

Prepare the substrates (made of SiO₂) for the collimating and deflectingmodule 3, the light-combining module 4 and the shaping module 5, andform the corresponding nanostructures (made of SiO₂) on the substratesvia a semiconductor etching technique according to the sizes calculated,so as to form the meta optical arrays. The manufacturing method iswell-understood in semiconductor fabrication, and will not be furtherdescribed. In this embodiment, the collimating and deflecting module 3needs three substrates, the light-combining module 4 needs onesubstrate, and the shaping module 5 shares the substrates of thecollimating and deflecting module 3, so four substrates are needed inthis embodiment.

Wherein, each of the collimating and deflecting meta optical members 31has a first surface 313 that is proximate to the light source modules 2,a second surface 314 that is opposite to the first surface 313 and thatis proximate to the light-combining meta optical member 40. The shapingmeta optical arrays 51 of the shaping module 5 are respectively formedon the first surfaces 313 of the collimating and deflecting meta opticalmembers 31. The collimating and deflecting meta optical array of each ofthe collimating and deflecting meta optical members 31 is formed on thesecond surface 314 of the collimating and deflecting meta optical member31.

The light-combining meta optical array of the light-combining metaoptical member 40 can be formed on an arbitrary surface of the substrate41. In this embodiment, the light-combining meta optical array is formedon a surface of the substrate 41 proximate to the collimating anddeflecting module 3. Referring to FIGS. 2, 13 and 14 , this embodimentis used in a projector 9. The projector 9 includes a MEMS(microelectromechanical systems) reflector 91 and a control circuit (notshown). The MEMS reflector 91 is controlled by the control circuit toreflect light beams emitted from the light-combining module 4, so thatthe light ray(s) 92 travels to a predetermined position and that adesired picture is obtained. In FIGS. 13 and 14 , a plurality of lightrays 92 are presented to illustrating different projecting positions.The projector 9 and the MEMS reflector 91 are well-understood in theart, and would not be further described.

Referring to FIG. 2 , according to the above, the advantages of theembodiment according to the disclosure are as follows:

1. By virtue of the collimating and deflecting meta optical member 31that collimates and deflects the light beams emitted by the light sourcemodules 2, and by virtue of the light-combining module 4 that receivesthe collimated light beams in different directions, and deflects thelight beams, so as to combine the light beams into a single light beam.Compared with the conventional optical engine, the number of componentsis reduced, the manufacturing precision and assembling precision areenhanced, and the volume of the optical engine is reduced. In addition,the meta optical members are made through a semiconductor fabricationtechnique, which has high manufacturing precision and high assemblingprecision compared with the manufacturing conventional opticalcomponents.

2. By virtue of the shaping module 5, the metalens-integrated opticalengine has a function of shaping light beams. Since the function ofshaping light beams are implemented by meta optical arrays, the volumeof the metalens-integrated optical engine is relatively small.

In the description above, for the purposes of explanation, numerousspecific details have been set forth in order to provide a thoroughunderstanding of the embodiments. It will be apparent, however, to oneskilled in the art, that one or more other embodiments may be practicedwithout some of these specific details. It should also be appreciatedthat reference throughout this specification to “one embodiment,” “anembodiment,” an embodiment with an indication of an ordinal number andso forth means that a particular feature, structure, or characteristicmay be included in the practice of the disclosure. It should be furtherappreciated that in the description, various features are sometimesgrouped together in a single embodiment, figure, or description thereoffor the purpose of streamlining the disclosure and aiding in theunderstanding of various inventive aspects, and that one or morefeatures or specific details from one embodiment may be practicedtogether with one or more features or specific details from anotherembodiment, where appropriate, in the practice of the disclosure.

While the disclosure has been described in connection with what areconsidered the exemplary embodiments, it is understood that thisdisclosure is not limited to the disclosed embodiments but is intendedto cover various arrangements included within the spirit and scope ofthe broadest interpretation so as to encompass all such modificationsand equivalent arrangements.

What is claimed is:
 1. A metalens-integrated optical engine comprising:a plurality of light source modules, each of the light source modulesemitting a light beam with particular wavelength; a collimating anddeflecting module including a plurality of collimating and deflectingmeta optical members each of which is located on the path of the lightbeam emitted by a respective one of the light source modules, thecollimating and deflecting meta optical members being for collimatingand deflecting the light beams emitted by the light source modules suchthat the light beams emitted by the light source modules are collimatedand deflected and travel to a predetermined position; and alight-combining module including a light-combining meta optical memberthat is located at one side of the collimating and deflecting moduleopposite to the light source modules, the light-combining meta opticalmember including a light-combining meta optical array that is located atthe predetermined position, that receives the light beams collimated anddeflected via the collimating and deflecting module, and that deflectsthe light beams based on wavelengths and angles of incidence, so as tocombine the non-parallel light beams into a single light beam.
 2. Themetalens-integrated optical engine as claimed in claim 1, wherein: eachof the collimating and deflecting meta optical members includes asubstrate that has a surface extending along an X-axis and a Y-axis, anda collimating and deflecting meta optical array that is disposed on thesurface, that permits incidence of the light beams emitted by therespective one of the light source modules, and that includes aplurality of nanostructures that are arranged in an array, each of thenanostructures extending along a Z-axis that is perpendicular to thesurface; the nanostructures of the collimating and deflecting metaoptical array of n-th collimating and deflecting meta optical membersatisfy a phase shift formula relative to a center of an optical axisΔφ_(nC)(x_(n), y_(n))=${- \frac{2\pi}{\lambda_{n}}}\left( {\sqrt{x_{n}^{2} + y_{n}^{2} + f_{n}^{2}} - f_{n} - {\left( {{x_{n}\cos\theta_{n}} + {y_{n}\sin\theta_{n}}} \right)\sin\gamma_{n}}} \right)$−ΔΦ_(nC)(x_(n), y_(n));${{{where}{{\Delta\Phi}_{nC}\left( {x_{n},y_{n}} \right)}} = {\frac{2\pi}{\lambda_{n}}{\sum_{i = 0}^{\infty}{\sum_{j = 0}^{\infty}{a_{nij}x_{n}^{2i}y_{n}^{2j}}}}}},{{{and}2i} +}$2j ≥ 4; n denotes all positive integers no greater than N, and N is thenumber of the collimating and deflecting meta optical members,Δϕ_(nC)(x_(n),y_(n)) denoting the phase shift of n-th light beamrelative to the center of an optical axis of the collimating anddeflecting meta optical array of n-th collimating and deflecting metaoptical member generated by the collimating and deflecting meta opticalarray of n-th collimating and deflecting meta optical member, an origin(0, 0) of the coordinate system being defined to be the center of theoptical axis of the collimating and deflecting meta optical array ofn-th collimating and deflecting meta optical member, Δϕ_(nC)(0,0)=0,(x_(n),y_(n)) denoting the position of each of the nanostructures of thecollimating and deflecting meta optical array of n-th collimating anddeflecting meta optical member in the coordinate system, λ_(n) being thewavelength of n-th light beam, f_(n) being the focal length of n-thlight beam, θ_(n) being the angle formed between the X-axis and theimaging light beam of n-th light beam, y_(n) being the angle formedbetween the Z-axis and the imaging light beam of n-th light beam,ΔΦ_(nC)(x_(n),y_(n)) being high-order term, and being for compensatingthe phase shift of high-order optical aberration, a_(nij) beingpredetermined coefficients.
 3. The metalens-integrated optical engine asclaimed in claim 1, wherein: the light-combining meta optical memberincludes a substrate that has a surface extending along an X-axis and aY-axis, and a light-combining meta optical array that is disposed on thesurface, that permits incidence of the light beams collimated anddeflected via the collimating and deflecting module, and that includes aplurality of nanostructures that are arranged in an array, each of thenanostructures extending along a Z-axis that is perpendicular to thesurface; each of the nanostructures of the light-combining meta opticalarray of the light-combining meta optical member satisfy the phase shiftformula relative to center of optical axis${{{\Delta\varphi}_{nL}\left( {x,y} \right)} = {\frac{2\pi}{\lambda_{n}}\left( {{x\cos\theta_{n}} + {y\sin\theta_{n}}} \right)\sin\gamma_{n}}};$n denotes all positive integers no greater than N, and N is the numberof the collimating and deflecting meta optical members, Δϕ_(nL)(x,y)denoting the phase shift of n-th light beam relative to the center ofoptical axis of the light-combining meta optical array generated by thelight-combining meta optical array, an origin (0, 0) of the coordinatesystem being defined to be the center of an optical axis of thelight-combining meta optical array, Δϕ_(nL)(0,0)=0, (x,y) denoting theposition of each of the nanostructures of the light-combining metaoptical array in the coordinate system. λ_(n) being the wavelength ofn-th light beam, θ_(n) being the angle formed between the X-axis and theincident light beam of n-th light beam, γ_(n) being the angle formedbetween the Z-axis and the incident light beam of n-th light beam. 4.The metalens-integrated optical engine as claimed in claim 3, whereinthe light-combining meta optical array is located at one side of thesubstrate of the light-combining meta optical member proximate to thecollimating and deflecting module.
 5. The metalens-integrated opticalengine as claimed in claim 1, further comprising a shaping module, theshaping module including a plurality of shaping meta optical arrays,each of the shaping meta optical arrays being disposed on a disposingsurface of a respective one of the collimating and deflecting metaoptical members, permitting incidence of the light beams emitted by therespective one of the light source modules, and including a plurality ofnanostructures that are arranged in an array, each of the shaping metaoptical arrays having a coordinate system that has an X-axis, a Y-axisand a Z-axis, and the disposing surface of the respective one of thecollimating and deflecting meta optical members extending along theX-axis and the Y-axis, each of the nanostructures extending along aZ-axis that is perpendicular to the disposing surface; wherein thenanostructures of n-th shaping meta optical array satisfy the phaseshift formula relative to center of optical axis${{\Delta\varphi}_{nS}\left( {x_{n},y_{n}} \right)} = {\frac{2\pi}{\lambda_{n}}\left( {\sqrt{x_{n}^{2} + f_{xn}^{2}} - f_{xn} + \sqrt{y_{n}^{2} + f_{yn}^{2}} - f_{yn}} \right)}$−ΔΦ_(nS)(x_(n), y_(n));${{{wherein}{{\Delta\Phi}_{nS}\left( {x_{n},y_{n}} \right)}} = {\frac{2\pi}{\lambda_{n}}{\sum_{i = 0}^{\infty}{\sum_{j = 0}^{\infty}{b_{nij}x_{n}^{2i}y_{n}^{2j}}}}}},{and}$2i + 2j ≥ 4; wherein, n denotes all positive integers no greater than N,and N is the number of the collimating and deflecting meta opticalmembers, Δϕ_(nS)(x_(n),y_(n)) denoting the phase shift of n-th lightbeam relative to the center of optical axis of n-th shaping meta opticalarray generated by n-th shaping meta optical array, an origin (0, 0) ofthe coordinate system being defined to be the center of an optical axisof n-th shaping meta optical array, Δϕ_(nS)(0,0)=0, (x_(n),y_(n))denoting the position of each of the nanostructures of n-th shaping metaoptical array in the coordinate system, λ_(n) being the wavelength ofn-th light beam, f_(xn) being the focal length of n-th light beam alongthe X-axis, f_(yn) being the focal length of n-th light beam along theY-axis, ΔΦ_(nS)(x_(n),y_(n)) being high-order term, and being forcompensating the phase shift of high-order optical aberration, b_(nij)being predetermined coefficients.
 6. The metalens-integrated opticalengine as claimed in claim 5, wherein each of the shaping meta opticalarrays of the shaping module is located at a first surface of therespective one of the collimating and deflecting meta optical membersthat is proximate to the light source modules, each of the collimatingand deflecting meta optical members including a collimating anddeflecting meta optical array that is formed on a second surface of thecollimating and deflecting meta optical member proximate to thelight-combining meta optical member and that is opposite to the shapingmeta optical arrays.
 7. A metalens-integrated optical engine comprising:a plurality of light source modules, each of the light source modulesemitting a light beam with particular wavelength; a collimating anddeflecting module including a plurality of collimating and deflectingmeta optical members each of which is located on the path of the lightbeam emitted by a respective one of the light source modules, thecollimating and deflecting meta optical members being for collimatingand deflecting the light beams emitted by the light source modules suchthat the light beams emitted by the light source modules are collimatedand deflected and travel to a predetermined position, each of thecollimating and deflecting meta optical members including a substratethat has a surface extending along an X-axis and a Y-axis, and acollimating and deflecting meta optical array that is disposed on thesurface, that permits incidence of the light beams emitted by therespective one of the light source modules, and that includes aplurality of nanostructures arranged in an array, each of thenanostructures extending along a Z-axis that is perpendicular to thesurface, wherein the nanostructures of the collimating and deflectingmeta optical array of n-th collimating and deflecting meta opticalmember satisfy a phase shift formula relative to a center of an opticalaxis Δφ_(nC)(x_(n), y_(n))=$- \frac{2\pi}{\lambda_{n}}\left( {\sqrt{x_{n}^{2} + f_{xcn}^{2}} - f_{xcn} + \sqrt{y_{n}^{2} + f_{ycn}^{2}} - f_{ycn} -} \right.$(x_(n)cos θ_(n) + y_(n)sin θ_(n))sin γ_(n)) − ΔΦ_(nC)(x_(n), y_(n));${{{wherein}{{\Delta\Phi}_{nC}\left( {x_{n},y_{n}} \right)}} = {\frac{2\pi}{\lambda_{n}}{\sum_{i = 0}^{\infty}{\sum_{j = 0}^{\infty}{a_{nij}x_{n}^{2i}y_{n}^{2j}}}}}},$and2i + 2j ≥ 4, wherein n denotes all positive integers no greater thanN, and N is the number of the collimating and deflecting meta opticalmembers, Δϕ_(nC)(x_(n),y_(n)) denoting the phase shift of n-th lightbeam relative to the center of an optical axis of the collimating anddeflecting meta optical array of n-th collimating and deflecting metaoptical member generated by the collimating and deflecting meta opticalarray of n-th collimating and deflecting meta optical member, an origin(0, 0) of the coordinate system being defined to be the center of theoptical axis of the collimating and deflecting meta optical array ofn-th collimating and deflecting meta optical member, Δϕ_(nC)(0,0)=0,(x_(n),y_(n)) denoting the position of each of the nanostructures of thecollimating and deflecting meta optical array of n-th collimating anddeflecting meta optical member in the coordinate system, λ_(n) being thewavelength of n-th light beam, f_(xcn) being the focal length of thecollimating and deflecting meta optical array along the X-axis, f_(ycn)being the focal length of the collimating and deflecting meta opticalarray along the Y-axis, θ_(n) being the angle formed between the X-axisand the imaging light beam of n-th light beam, γ_(n) being the angleformed between the Z-axis and the imaging light beam of n-th light beam,ΔΦ_(nC)(x_(n),y_(n)) being high-order term, and being for compensatingthe phase shift of high-order optical aberration, α_(nij) beingpredetermined coefficients; a shaping module including a plurality ofshaping meta optical arrays, each of the shaping meta optical arraysbeing disposed on a disposing surface of a respective one of thecollimating and deflecting meta optical members for shaping the lightbeams emitted by the respective one of the light source modules; and alight-combining module receiving the light beams collimated anddeflected via the collimating and deflecting module, and combining thenon-parallel light beams into a single light beam.
 8. Themetalens-integrated optical engine as claimed in claim 7, wherein: forthe collimating and deflecting meta optical array of each of thecollimating and deflecting meta optical members and the respective oneof the shaping meta optical arrays, the relationship among the focallengths f_(xcn), f_(ycn) of the collimating and deflecting meta opticalarray and the focal lengths f_(xn), f_(yn) of the shaping meta opticalarray are:${f_{ycn} = \frac{d \cdot {f_{ytn}\left( {d - f_{xn}} \right)}}{{f_{ytn}\left( {d - f_{xn}} \right)} - {f_{xn}\left( {d - f_{xtn}} \right)}}};$${f_{xn} = \frac{f_{xcn} - d}{\frac{f_{xcn}}{f_{xtn}} - 1}};$${f_{yn} = \frac{d \cdot {f_{xn}\left( {d - f_{xtn}} \right)}}{{d\left( {d - f_{ytn}} \right)} - {f_{xn}\left( {f_{xtn} - f_{ytn}} \right)}}};$f_(xtn), f_(ytn) are synthesized focal lengths respectively along X-axisand Y-axis synthesized by the collimating and deflecting meta opticalarray and the shaping meta optical array, and d is equivalent airthickness between the collimating and deflecting meta optical array andthe shaping meta optical array.
 9. The metalens-integrated opticalengine as claimed in claim 7, wherein: each of the shaping meta opticalarrays receives the light beams emitted by the respective one of thelight source modules, and including a plurality of nanostructures thatare arranged in an array, each of the shaping meta optical arrays havinga coordinate system that has an X-axis, a Y-axis and a Z-axis, each ofthe nanostructures extending along a Z-axis that is perpendicular to thesurface; the nanostructures of n-th shaping meta optical array satisfythe phase shift formula relative to center of optical axis${{\Delta\varphi}_{nS}\left( {x_{n},y_{n}} \right)} = {\frac{2\pi}{\lambda_{n}}\left( {\sqrt{x_{n}^{2} + f_{xn}^{2}} - f_{xn} + \sqrt{y_{n}^{2} + f_{yn}^{2}} - f_{yn}} \right)}$−ΔΦ_(nS)(x_(n), y_(n));${{{where}{{\Delta\Phi}_{nS}\left( {x_{n},y_{n}} \right)}} = {\frac{2\pi}{\lambda_{n}}{\sum_{i = 0}^{\infty}{\sum_{j = 0}^{\infty}{b_{nij}x_{n}^{2i}y_{n}^{2j}}}}}},{{{and}2i} +}$2j ≥ 4; n denotes all positive integers no greater than N, and N is thenumber of the collimating and deflecting meta optical members,Δϕ_(nS)(x_(n),y_(n)) denoting the phase shift of n-th light beamrelative to the center of optical axis of n-th shaping meta opticalarray generated by n-th shaping meta optical array, an origin (0, 0) ofthe coordinate system being defined to be the center of optical axis ofn-th shaping meta optical array, Δϕ_(nS)(0,0)=0, (x_(n),y_(n)) denotingthe position of each of the nanostructures of n-th shaping meta opticalarray in the coordinate system, λ_(n) being the wavelength of n-th lightbeam, f_(xn) being the focal length of n-th light beam along the X-axis,f_(yn) being the focal length of n-th light beam along the Y-axis,ΔΦ_(nS)(x_(n),y_(n)) being high-order term, and being for compensatingthe phase shift of high-order optical aberration, b_(nij) beingpredetermined coefficients.
 10. The metalens-integrated optical engineas claimed in claim 7, wherein the collimating and deflecting metaoptical arrays of each of the collimating and deflecting meta opticalmembers is formed on a surface of the collimating and deflecting metaoptical member proximate to the light-combining meta optical member, andeach of the shaping meta optical arrays of the shaping module is locatedat another surface of the respective one of the collimating anddeflecting meta optical members that is proximate to the light sourcemodules.